Lappin's first Norwich goal in almost five years and a second-half penalty from Hoolahan proved just enough to see off League One outfit Scunthorpe, who had seen Mark Duffy equalise with a superb 30-yard effort.
It was the visitors who made the brightest start to the game and winger Andy Barcham could have put them ahead as early as the third minute.
The former Tottenham youngster wriggled free in the Norwich penalty area before forcing a reaction save out of Declan Rudd.
Norwich then came close moments later but neither Steve Morison nor Michael Turner could make a telling connection to David Fox's inswinging corner.
Chris Martin's speculative bicycle kick failed to hit the target with the game lacking a cutting edge in the opening exchanges.
The Canaries had managed to establish a level of dominance by the half hour mark and were rewarded with the opening goal soon after.
Andrew Surman played a pass in field to Lappin who took a touch before firing past Sam Slocombe in the Scunthorpe goal from 25 yards out.
Alan Knill's side have lost all three of their League One games so far this season but they did not let their heads drop and were level two minutes later.
Christian Ribeiro picked out Duffy who curled in an effort from 30 yards that went in off the inside of the post with Rudd well beaten.
Norwich were nearly back in front soon after but defender Ryan Bennett headed Surman's corner just wide of the post under pressure from two Scunthorpe defenders.
With the game approaching half-time Scunthorpe were arguably the better side but a mix-up between Slocombe and Ribeiro from a Hoolahan cross almost gave the Premier League side the lead but the loose ball bounced clear.
The home side made the better start to the second half and another chance fell to Lappin but his shot was bravely blocked by Iron defender David Mirfin.
Lappin took a knock during the challenge and was unable to continue, with Chris Hughton introducing Anthony Pilkington in his place.
Norwich were not disrupted by the change and were back in front after 55 minutes.
Hoolahan was brought down in the area by Niall Canavan after a neat interchange with Morison and the Canaries' skipper picked himself up and duly converted the penalty.
The second goal seemed to give Norwich the impetus and they came close to a third moments later as Surman fired the ball across goal from a tight angle with Slocombe only able parry his effort into the middle of the penalty area, although the ball was cleared before a Norwich player could latch onto it.
Scunthorpe were still showing signs of getting back into the game as Mike Grella beat the offside trap and drew a smart save from Rudd with just over 25 minutes remaining.
Norwich full-back George Francomb fired just wide of Slocombe's far post when he was picked out by Fox while unattended on the edge of the Scunthorpe penalty area with the Canaries starting to keep hold of the ball for longer spells.
The hosts should have scored a decisive third goal 15 minutes from time but Surman headed Marc Tierney's cross straight into the arms of Slocombe.
Scunthorpe almost punished Norwich for their wastefulness in front of goal as Rudd was forced to tip over a spectacular long-range volley from debutant David Prutton.
The former Nottingham Forest man's effort was the last real attacking threat offered by Knill's side with Norwich taking the sting out of the game in the final 10 minutes.
The five minutes of stoppage time signalled by the fourth official would have given Scunthorpe some hope but Norwich kept possession expertly to secure their safe progression into the third round of the competition.